Carl Jenkinson's tame back header was prodded home by Cesar Azpilicueta midway through the first half.
Jose Mourinho chose to forego the post-match press conference at the Emirates, with assistant first-team coach Steve Holland instead facing the media.
"I think it's been a satisfying three days," he said after the Blues followed up Sunday's 2-1 win against Manchester City with another victory.
"You're not just talking about a team. The objective at Chelsea is always to compete in all four competitions.
"Given we had to play the game tonight, which I know Jose has documented was far from ideal with one day between the matches, it gave us no choice really but to use the full squad.
"Every player in the squad deserves great credit for their performances in the three days."
For the big stories and the banter follow us on Twitter: @tribalfootball